Konferenz: Workshop on Mathematics in Finance


Measuring extremal dependence in financial time series

{{_Ltalk:R}} Prof. Dr. Thomas Mikosch
Datum: 18.10.13   Zeit: 10.00 - 10.50   Raum: Y27H46

Covariances are not very meaningful if one wants to study the extremes in a non-Gaussian time series. However, the tail dependence coefficient of a two-dimensional vector has been studied in quantitative risk management for a long time (see e.g. the book by McNeil, Frey and Embrechts): it can be interpreted as the limiting correlation of the indicator functions of the extreme event that both components of the vector are large at the same time. Starting from this observation, one can introduce an asymptotic autocorrelation function for extreme events in a time series, the extremogram. The extremogram is essentialy dimensionless and can be defined for multivariate or even function-valued data. Based on this idea, the notions of classical time series analysis enter: short and long range dependence, autocorrelation function, spectral distribution and their statistical counterparts such as the sample extremogram and the periodogram of the extreme events in a series. We explain the underlying theory and illustrate how the theory works on financial time series.

This is joint work with Richard A. Davis (Columbia) and Yuwei Zhao (Copenhagen).